Manual version Calculation of Section Properties for I-section

Transcription

1 Manual Manual version Calculation of Section Properties for I-section 1. Overview The object of this manual is to explain the usage of calculation page in this site, so the explanation of the theory of computation is basically neglected. It assumes as a user who understands enough about the theory of computation. The program is intended to calculate section properties for I-section. In this context I-section means a shape of cross section that has 3 elements which are composed from two horizontal plates (upper flange and lower flange) and a vertical plate(web) linking to flanges. Actually it can be calculated even if there are 1 or 2 in these elements. Fig.1 3 elements of I-section Section properties for horizontal axis(in general strong axis), for vertical axis (In general weak axis), and for main axes(synergistic axis) are calculable. Section properties obtained in the calculation are sectional area, centroid, moment of inertia, section modulus and radius of gyration. Calculating result and cross section image with dimensions are displayed on screen. In addition, the calculating result can be outputted as a text file, and the section image as a image file. 2. Screen Screen is generally formed from 3 blocks, "Inputs", "Processings" and "Outputs". "Inputs" block is used to input the size of plates. "Processings" block is used to command of processing such as calculation. "Outputs" block is used to display the calculation result. Well, a image at right-under of screen is a mere decoration. Fig.2 formation of screen 3. Inputs block Inputs block is composed from 3 subblocks, "Sizes", Output length of decimal figures and Calculation ranges. (1) Sizes subblock By radio button, the unit of sizes can be chosen from mm, cm, m and inch. By this, displayed unit on the screen changes all at once. However, though the unit is changed output values are not converted. The sizes of plates forming I-section and eccentric values of upper and lower flanges are inputted in each text box. At initial the positions of size symbols are shown at bottom right corner on screen, so please refer when you input. Eccentric value indicates the relativistic position between flange and web. It is combined with indicating types as eu 1 Fig.3 inputted sizes

2 for upper flange and as ed for lower flange. The flange s eccentricity has no relation when the calculation for horizontal axis is only executed. In this case the calculation result is not changed even if any value is inputted for the flange s eccentricity. The flange s eccentricity has relation when the calculation for vertical axis is executed. For upper flange and lower flange, the indicating type(a,b,c) is selected from each combo-box. Each eccentric value is inputted in text-box at right of combo-box. Please refer Table 1. In right side column of Table 1, the case which both upper and lower eccentric value=0 are shown, but you can select for each. The type a indicates a distance between web center and flange center. When flange s center is right from web center, the value is positive. In case of eccentric value=0, flange is connected to web in the position of line symmetry for web. The type b indicates a distance between left side of web and left edge of flange. When flange s left edge is left from left side of web, the value is positive. In case of eccentric value=0, left edge of flange fits in left side of web. The type c indicates a distance between right side of web and right edge of flange. When flange s right edge is right from right side of web, the value is positive. In case of The indicating type eccentric value=0, right edge of flange fits in right side of web. Though any type can be represented same eccentricity, you may choice most easy type depending on the cross section. (2) output range of decimal figures subblock The output range of decimal figures can be select in each combo-box per dimension of unit. But the value indicated as decimal figure is the case which it is less than 10 6 (million) in absolute. 2 a b c how to take the eccentric value when flange s center is right from web center, the value is positive. when flange s left edge is left from left side of web, the value is positive. shape of eccentric value=0 when flange s right center is right from right side of web, the value is positive. Table 1. instructions of flange s eccentricity

3 The larger value is shown by index number to three decimal places, for example 1.234e+7 in which e+7 means The default number of decimal places is 1 for 1 dimension(length) but another all 0. You should arrange these numbers depending on the displayed output. By changing decimal number, input values are changed together. Therefore on the case of decreasing decimal number, it may occur that the value already inputted is changed by round off. For example, the input value 1.6 is changed to 2 by changing decimal number from 1 to 0. In this case, if decimal number is returned to 1, the value change to 2.0 not 1.6. So, please be caution about it. (3) calculation ranges subblock The calculation range is selected from following 3 check boxes. for horizontal(strong) axis for vertical(week) axis for main axis(on the necessity for calculation, all ranges are calculated.) This choice affects output range of Output block. For example, if you want only the calculated values for horizontal axis, please check only its check box. Furthermore, selecting for main axial, calculations for horizontal and vertical are executed too. 4. Processings block Following 6 processings are shown on buttons. When cursor moveover each button, button s color changes and the content of processing is simply shown. (1) Calculation It executes the calculation and displays the result to Outputs block together with the shape and dimensions of cross section with centroid axes. In addition, centroids are calculated as that determining the origin to the cross point of upper side of upper flange and centerline of web, h(horizontal) axis is positive to right and v(vertical) axis is positive to down. (2) Calculation Sheet It displays the calculation result, and saves it as a text file to client s computer. Clicking this button, the dialog(fig.5) is displayed. If you want to see the output before file-save, please click open button. Or if you not want to do so, please click save button, then the data can be directly saved. An example output is shown in Table 2. In order to align the sequence of characters, MS Gothic font with constant width is used as default font. 3 Fig.4 Centroid axes for calculation Fig.5 Dialog box for download of calculation sheet Sorry, this is the image for Japanese version. Would anyone supply to me the one for English version.

4 Please note that if the font with different width is used, characters are no longer aligned. In addition, please consider font size and line spacing too. The output in Microsoft Word format is not available(also ruled line and superscript). But you can make Word document trimming the appearance from the text file of calculation result and the gif file of cross-section, a little cumbersome by manual handling, like Table.3. In future I wish to make Word document like this with one click. (3) Save Sec. Image In fact, this button is a one just to explain how to save. Actually please do as following. Moreover cursor on the sectional figure and right click. click Name and save image The sectional figure is saved as a gif file. Fig.6 is a sample of the cross section. (4) Manual This manual is shown. (5) Reset Screen returns to its initial state. Therefore, input data in screen is eliminated. Fig.6 example of cross-section image (6) Return Screen closes the calculation site, and returns to the home site. 5. Outputs block Although Outputs block does not show the sub-block names, it is consisted from 3 subblocks, calculation table, display section properties and view of cross-section. Clicking of Calculation button, these displays are refreshed. (1) calculation table subblock In calculation table, the data to be required for calculation of section properties is outputted. By Calculation Ranges in Inputs block, the values only to be needed for calculation are displayed by numbers separated by 3 digits. But in the case that the value is larger than 10 6 (million), it is indicated by index to three decimal places, for example 1.234e+7 in which e+7 means Formula in each cell of this table can be seen as green characters by moveovering cursor on the cell. Each variable used in the formula is combined the size or symbol of section property and subscript of plate. Foe example, tu is a combination of t:thickness and u:upper flange. In addition, the formula of centroid of vertical axis:ch is changed by selection of indicating type of eccentricity. (2) display section properties subblock The values of section properties are displayed. View of for horizontal axis, for vertical axis and for main axis is changed by selecting radio button upward of it. (3) view of cross section subblock When this page is started or reset and input error occurs, explanation (see Fig.3) is displayed. 4

5 Excusing calculation, the cross section image is displayed in proportion to input size. The scaling is automatically adjusted in order to pack into the drawing area. In subblocks calculation table and display section properties, values are displayed with specified decimal point. But lower level 0 of decimal is neglected in order to avoid cumbersome. For example, when the number 12.3 is indicated by decimal place at 3, in calculation table and display section properties, it is shown as , but in cross section view, it is shown as

6 Section Properties for I-section for horizontal axis thickness breadth sectional vertical static second self area centroid moment moment inertia t mm b mm A mm2 v mm Mv mm3 Dv mm4 iv mm4 upper flange u e e+6 web w , e e+6 lower flange d , e e+6 total t , e e+6 height of section hv = tu + bw + td = 67.7 mm sectional area At = 503 mm2 vertical centroid from top surface cu = Mvt / At = 39.6 mm vertical centroid from bottom surface cd = hv - cu = 28.1 mm moment of inertia Iv = Dvt + ivt - At cu^2 = 386,815 mm4 section modulus at top surface Zu = Iv / cu = 9,772 mm3 section modulus at bottom surface Zd = Iv / cd = 13,758 mm3 radius of gyration rv = (Iv / At) = 27.7 mm for vertical axis thickness breadth sectional horizontal static second self area centroid moment moment inertia t mm b mm A mm2 h mm Mh mm3 Dh mm4 ih mm4 upper flange u ,120 9,800 17,067 web w lower flange d ,969 17,227 46,875 total t ,027 64,020 breadth of section bh = 62.5 mm sectional area At = 503 mm2 horizontal centroid from web center ch = Mvt / At = -1.7 mm horizontal centroid from left edge cl = 32.1 mm horizontal centroid from right edge cr = 30.4 mm moment of inertia Ih = Dht + iht - At ch^2 = 89,614 mm4 section modulus at left edge Zl = Ih / cl = 2,795 mm3 section modulus at right edge Zr = Ih / cr = 2,944 mm3 radius of gyration rh = (Ih / At) = 13.3 mm for main axis thickness breadth sectional vertical horizontal second area centroid centroid moment t mm b mm A mm2 v mm h mm Db mm4 upper flange u ,792 web w lower flange d ,855 total t ,063 centrifugal moment Ib = Dbt + ibt - At cu ch = -125,705 mm4 maximum moment of inertia Imax = (Iv+Ih)/2 + {(Iv-Ih)^2/4 +Ib} = 432,852 mm4 minimum moment of inertia Imin = (Iv+Ih)/2 - {(Iv-Ih)^2/4 +Ib} = 43,577 mm4 section modulus at left edge Zl = Ih / cl = 2,795 mm3 section modulus at right edge Zr = Ih / cr = 2,944 mm3 angle of principal axi φ = [arctan{2ib/(iv-ih)}]/2 = -20 maximum radius of gyration rmax = (Imax / At) = 29.3 mm minimum radius of gyration rmin = (Imin / At) = 9.3 mm Table 2.example of output sheet font:msgothic 10 point line spacing:fixed 12pt 6

7 Section Properties for I-section for horizontal axis upper flange u thickness breadth sectional area centroid static moment second moment self inertia t mm b mm A mm 2 v mm Mv mm 3 Dv mm 4 iv mm , e e e+9 web w , e e e+9 lower flange d , e e e+9 total t 27, e e e+9 height of section hv = tu + bw + td = 67.7 mm sectional area At = 503 mm2 vertical centroid from top surface cu = Mvt / At = 39.6 mm vertical centroid from bottom surface cd = hv - cu = 28.1 mm moment of inertia Iv = Dvt + ivt - At cu^2 = 386,815 mm4 section modulus at top surface Zu = Iv / cu = 9,772 mm3 section modulus at bottom surface Zd = Iv / cd = 13,758 mm3 radius of gyration rv = (Iv / At) = 27.7 mm table 3.example trimming in Word and adding the cross section image 7